[tex]\sin3\theta=\sin(\theta+2\theta)=\sin\theta\cos2\theta+\cos\theta\sin2\theta[/tex]
[tex]=\sin\theta(1-2\sin^2\theta)+2\cos^2\theta\sin\theta[/tex]
[tex]=\sin\theta-2\sin^3\theta+2(1-\sin^2\theta)\sin\theta[/tex]
[tex]=3\sin\theta-4\sin^3\theta[/tex]
